A conformally invariant Oseen equation for flow at small Reynolds numbers

Abstract

Starting from a complex variable formulation of the exact Navier-Stokes equations for the steady two-dimensional motion of an incompressible viscous fluid, a Burgers type linearization is introduced at small Reynolds number which results in a conformally invariant Oseen equation. The independent variables are the velocity potential and stream function for the corresponding irrotational flow. There are certain analytical advantages in this approach for the determination of uniformly valid approximations to flow at small Reynolds numbers and the method is illustrated by various examples.